Design optimality for treatment comparison experiments has been intensively studied by numerous researchers, employing a variety of statistically sound criteria. Their general formulation is based on the idea that optimality functions of the treatment information matrix are invariant to treatment permutation. This implies equal interest in all treatments. In practice, however, there are many experiments where not all treatments are equally important. When selecting a design for such an experiment, it would be better to weight the information gathered on different treatments according to their relative importance and/or interest. This dissertation develops a general theory of weighted design optimality, with special attention to the block design problem. Among others, this study develops and justifies weighted versions of the popular A, E and MV optimality criteria. These are based on the weighted information matrix, also introduced here. Sufficient conditions are derived for block designs to be weighted A, E and MV-optimal for situations where treatments fall into two groups according to two distinct levels of interest, these being important special cases of the "2-weight optimality" problem. Particularly, optimal designs are developed for experiments where one of the treatments is a control. The concept of efficiency balance is also studied in this dissertation. One view of efficiency balance and its generalizations is that unequal treatment replications are chosen to reflect unequal treatment interest. It is revealed that efficiency balance is closely related to the weighted-E approach to design selection. Functions of the canonical efficiency factors may be interpreted as weighted optimality criteria for comparison of designs with the same replication numbers. / Ph. D.

This work examines various asymptotic edge-decomposition problems on graphs. A G-group divisible design (G-GDD) of type [g_1, ..., g_u] and index lambda is a decomposition of the edges of the complete lambda-fold multipartite graph H, with groups (maximal independent sets) G_1, ..., G_n, |G_i| = g_i, into graphs (blocks) isomorphic to G. We shall also examine special types of G-GDDs (such as G-frames) and prove that, given all parameters except u, these structures exist for all asymptotically large u satisfying the necessary conditions. Our primary technique is to invoke a useful theorem of Lamken and Wilson on edge-colored graph decompositions. The basic construction for k-RGDDs shall be outlined at the end of the thesis.

This thesis consists of five chapters, based on four different articles. All of them are devoted to different aspects of spatial heterogeneity and its impact on economic equilibrium in space. The concept of heterogeneous continuous space is discussed in the introductory chapter.The first model "Equilibrium in Continuous Space under Decentralized Production" addresses the issue of the impact of differences across locations in exogeneous productivity on the structure of equilibrium prices, production and trade. The goal is to describe the general equilibrium in a spatially decentralized economy, when production, consumption and markets are distributed in continuous space and transportation costs are essentially linear. It is shown that an autarky equilibrium can exist only if transport costs are high enough. In the general case, the general equilibrium in this model includes some endogeneously determined trade areas, with flows of goods across space, and autarky areas where production and consumption activities take place only at the same point. An analytical solution in explicit functions is obtained; it contains equilibrium prices, labor supply and flows of goods as functions of the spatial variable. The model can be applied to a set of practical questions in regional economics. In particular, it is able to describe persistent price differentials across regions and non-local consequences of road construction and transportation cost shocks for the economy. The differences across locations in population density may have either historical or economic reasons.The second model "Hotelling's Revival" extends a well-known research of H.Hotelling (1929) to the two-dimensional case with spatially heterogeneous demand density, preserving the rest of his classical assumptions. It is shown that the problem of demand discontinuity in the one-dimensional model, which was discovered by d'Aspremont, Gabszewich and Thisse (1979), disappears in this case. This also holds for any bounded distribution of consumers on any compact set on a plane, which can describe real geographical situations. Demand continuity still holds for any transport costs, strictly increasing in distance and not necessarily linear. Although this is sufficient for the existence of Nash equilibrium in mixed strategies, in pure strategies it exists only for some subset of cases. Examples of both existence and non-existence are constructed, and for some family of densities the separation point between the two cases is found.The third model addresses locational choice of heterogeneous consumers, when land is also heterogeneous in quality. It is based on two articles. The first, "Dacha Pricing", is presented in chapter 4 and studies the problem of locational rent in a city-neighbourhood when utility includes both the impact of transport costs and time for transportation. For the case of identical agents the problem is solved explicitly and comparative statics with respect to exogeneous changes in transport cost and speed is studied. For the case of agents who are heterogeneous with respect to their income, a solution is also obtained. The model explains some evidence about dacha pricing in Russia and its dynamics during the transition period. The second article related to this model is "Location and Land Size Choice by Heterogeneous Agents". It generalizes the first one and form a separate chapter 5. A new approach about the general equilibrium allocation of heterogeneous divisible good (like land) among a continuum of heterogeneous consumers is proposed. The model is based on continuity of primitives which allow not only to finding a general equilibrium solution in a class of continuous functions, but also to treat the solution to a continuous problem as the limit of the corresponding sequence of discrete problems. This solves one of Berliant's paradoxes, related to spatial economics. The multiplicity of equilibria is shown to take place.

Made available in DSpace on 2015-05-15T11:46:25Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 450936 bytes, checksum: 7e53189000f5416171ee58a4623b8aa6 (MD5) Previous issue date: 2010-02-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Bertholf and Walls provided a characterization for the class of groups quasi-injective finite. Furthermore, Juriaans, Bastos Azevedo and give a rating for the injective type groups, which are a distinct class of the former despite being quite close. / Bertholf e Walls forneceram uma caracterização para a classe de grupos quasi-injetivos finitos. Além disso, Juriaans, Bastos e Azevedo dão uma classificação para os grupos do tipo injetivo, os quais são uma classe distinta da anterior apesar de serem bastante próximas.

La publicación congrega a reconocidos abogados peruanos que son especialistas vinculados al Derecho de las Obligaciones. Los temas desarrollados por los autores del libro cuentan con una posición propia respecto a las modalidades, efectos e inejecución del Derecho de las Obligaciones, lo cual enriquece a esta obra, dividida en tres partes, por las distintas perspectivas sobre temas puntuales del ámbito profesional y académico. / The book brings together recognized peruvian lawyers linked to the Law of Obligations. The themes developed by the authors of the book have its own points of view over the modes, effects and non-implementation of the Law of Obligation. The perspectives of specific issues of the professional field and academic of the law increase the important of this publication divided in three parts.

The statistical modeling of extreme natural hazards is becoming increasingly important due to climate change, whose effects have been increasingly visible throughout the last decades. It is thus crucial to understand the dependence structure of rare, high-impact events over space and time for realistic risk assessment. For spatial extremes, max-stable processes have played a central role in modeling block maxima. However, the spatial tail dependence strength is persistent across quantile levels in those models, which is often not realistic in practice. This lack of flexibility implies that max-stable processes cannot capture weakening dependence at increasingly extreme levels, resulting in a drastic overestimation of joint tail risk. To address this, we develop new dependence models in this thesis from the class of max-infinitely divisible (max-id) processes, which contain max-stable processes as a subclass and are flexible enough to capture different types of dependence structures. Furthermore, exact simulation algorithms for general max-id processes are typically not straightforward due to their complex formulations. Both simulation and inference can be computationally prohibitive in high dimensions. Fast and exact simulation algorithms to simulate max-id processes are provided, together with methods to implement our models in high dimensions based on the Vecchia approximation method. These proposed methodologies are illustrated through various environmental datasets, including air temperature data in South-Eastern Europe in an attempt to assess the effect of climate change on heatwave hazards, and sea surface temperature data for the entire Red Sea. In another application focused on assessing how the spatial extent of extreme precipitation has changed over time, we develop new time-varying $r$-Pareto processes, which are the counterparts of max-stable processes for high threshold exceedances.

In the paper [HSS] Herrlich, Salicrup and Strecker were able to show that Kuratowski / Mrowka's Theorem concerning compactness for topological spaces could be applied to a wider setting. In this dissertation, which is based on the paper [F subscript 1], we interpret Kuratowski / Mrowka's result in the category R-Mod. Chapter One deals mainly with the preliminary definitions and results and we also show that there is a 1-1 correspondence between torsion theories and standard factorisation systems. In Chapter Two we, obtain for every torsion theory T, a theory of T-compactness which is an extension of the definition of compactness found in [HSS]. We then obtain a characterisation of T-compactness under certain conditions on the ring R and torsion theory T. In Chapter Three we examine the class of T-compact R-modules more closely when the ring R is T-hereditary and T-noetherian. We also obtain further characterisation of T-compactness under these additional conditions. In Chapter Four we show that many topological results have analogues in R-Mod. / Mathematical Sciences / M. Sc. (Mathematics)

Dans cette thèse, nous étudions la géométrie analytique p-adique et la cohomologie l-adique de certains espaces de Rapoport-Zink, en utilisant la théorie des filtrations de Harder-Narasimhan des schémas en groupes finis et plats élaborée par Fargues.Cette thèse se compose de trois parties. La première partie traite de certains espaces de Rapoport-Zink non-basiques, qui satisfont à la condition que leur polygone de Newton et polygone de Hodge ont un point de contact non-trivial, qui est un point de rupture pour le polygone de Newton. Sous cette hypothèse, nous prouvons que ces espaces de Rapoport-Zink peuvent être décomposés en une somme directe d'espaces de modules des types de Rapoport-Zink associés à certains sous-groupes paraboliques appropriés, donc leurs cohomologie l-adique sont des induites paraboliques et en particulier ne contiennent pas de représentations supercuspidales. Nous prouvons ces faits en démontrant d'abord un théorème sur la filtration de Hodge-Newton pour les groupes p-divisibles avec des structures additionelles sur des anneaux de valuation complets de rang un et de caractéristique mixte (0,p).Dans la deuxième partie, nous considérons les espaces de Rapoport-Zink basiques de signature (1,n-1) pour les groupes unitaires associés à l'extension quadratique non ramifiée de Qp. On étudie l'action de Hecke sur ces espaces en détails. En utilisant la théorie des filtrations de Harder-Narasimhan des schémas en groupes finis et plats, et la stratification de Bruhat-Tits de la fibre spéciale réduite Mred étudié par Vollaard-Wedhorn, on trouve un certain domaine analytique compact DK telle que ses itérés dans le groupe G(Qp)×Jb(Qp) forme un recouvrement localement fini de tout l'espace MK. Nous appelons un tel phénomène une décomposition cellulaire localement finie.Dans la troisième partie, nous démontrons une formule de Lefschetz pour ces espaces pour l'action des éléments semi-simples réguliers elliptiques, en tenant compte de l'action de ces éléments sur les cellules et en appliquant le théorème principal de Mieda. De la même manière, nous pouvons aussi reprouver la formule de Lefschetz pour les espaces de Lubin-Tate précédemment obtenue par Strauch et Mieda. Cette formule de Lefschetz devrait caractériser la réalisation de correspondances de Jacquet-Langlands locales pour les groupes unitaires dans la cohomologie l-adique de ces espaces de Rapoport-Zink, dès que certains problèmes correspondants de théorie des représentations auront été résolus. / In this thesis we study p-adic analytic geometry and l-adic cohomology of some Rapoport-Zink spaces, using the theory of Harder-Narasimhan filtration of finite flat group schemes developed by Fargues .This thesis consists of three parts. The first part deals with some non-basic Rapoport-Zink spaces, which satisfy the condition that their Newton polygon and Hodge polygon have a non-trivial contact point, which is a breakpoint for the Newton polygon. Under this hypothesis, we prove these Rapoport-Zink spaces can be decomposed as a direct sum of smaller Rapoport-Zink spaces associated to some suitable parabolic subgroups, thus their l-adic cohomology is parabolically induced and in particular contain no supercuspidal representations. We prove these facts by first proving a theorem about the Hodge-Newton filtration for p-divisible groups with additional structures over complete valuation rings of rank one and mixed characteristic (0,p).In the second part, we consider the basic Rapoport-Zink spaces with signature (1,n-1) for the unitary groups associated to the unramified quadratic extension of Qp. We study the Hecke action on these spaces in details. By using the theory of Harder-Narasimhan filtrations of finite flat group schemes, and the Bruhat-Tits stratification of the reduced special fiber Mred studied by Vollaard-Wedhorn, we find some compact analytic domain DK such that its translates under the group G(Qp)×Jb(Qp) form a locally finite cover of the whole space MK. We call such a phenomenon a locally finite cell decomposition.In the third part we prove a Lefschetz trace formula for these spaces for the action of regular semi-simple elliptic elements, by considering the action of these elements on the cells and applying Mieda's main theorem. In the same way we can also reprove the Lefschetz trace formula for Lubin-Tate spaces as previously obtained by Strauch and by Mieda. This Lefschetz trace formula should characterize the realization of local Jacquet-Langlands correspondences for unitary groups in the l-adic cohomology of these Rapoport-Zink spaces, as soon as some corresponding representation theoretic problems are solved.

[pt] O problema de escalonamento de tarefas divisíveis consiste em determinar como uma carga a ser processada deve ser dividida entre processadores e em que ordem cada fração de carga será enviada a cada processador. Considera-se o escalonamento em redes estrela com computadores e enlaces heterogêneos. Nesta dissertação são propostas formulações originais deste problema como modelos de programação linear inteira mista, assim como um novo algoritmo de complexidade O(n) para a solução ótima de um caso especial. Além disso, também são propostas duas novas heurísticas para o problema, que permitem a elaboração de bons escalonamentos para instâncias de grande porte em um reduzido tempo de processamento. / [en] The problem of divisible job scheduling consists of determining how to divide the data to be processed among processors and in which order each fraction should be sent to them. In this dissertation, we consider the divisible load scheduling problem in star networks with heterogeneous computers and links. Original mixed integer linear programming formulations of this problem are proposed, as well as a new algorithm with complexity O(n) to find the optimal solution for a special case. We also propose two fast heuristics that achieve good results for instances representing large scale computing systems.

在本篇論文中我們使用矩陣來建構可分組設計(GDD), 我們列出了兩種型 式的建構, 第一種 -- 起因於 W.H. Haemers -- A .crtimes. J + I .crtimes. D, 利用此種建構我們將所有符合 r - .lambda.1 = 1 的 (m,n,k,.lambda.1,.lambda.2) GDD 分成三類: (i) A=0 或 J-I, (ii) A 為 .mu. - .lambda. = 1 強則圖的鄰接矩陣, (iii) J-2A 為斜對稱 矩陣的核心。第二種型式為 A .crtimes. D + .Abar .crtimes. .Dbar ,此種方法可以建構出 b=4(r-.lambda.2) 的正規和半正規 GDD 。另外在 論文中, 我們研究在這些建構中出現的相關題目。 / In this thesis we use matrices to construct group divisible designs (GDDs). We list two type of constructions, the first type is -- due to W.H. Heamers -- A .crtimes. J + I .crtimes. D and use this construction we classify all the (m,n,k,. lambda.1, .lambda.2) GDD with r - .lambda.1 = 1 in three classes according to (i) A = 0 or J-I, (ii) A is the adjacency matrix of a strongly regular graph with .mu. - .lambda. = 1, (iii) J - 2A is the core of a skew-symmetric Hadamard matrix. The second type is A .crtimes. D + .Abar .crtimes. .Dbar , this type can construct many regular and semi-regular GDDs with b=4(r-.lambda.2). In the thesis we investigate related topics that occur in these constructions.